Find the sum to n terms of the series 3 - 12-5 - 22-7 - 32-

The given series is 3 ×12 + 5 × 22 + 7 × 32 + … nth term, an = ( 2n + 1) n2 = 2n3 + n2 ...

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nth Term of A.P

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Question

Find the sum to n terms of the series 3 × 1² + 5 × 2² + 7 × 3² + …

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Solution

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n

\frac{3}{1^{2} \cdot 2^{2}} + \frac{5}{2^{2} \cdot 3^{2}} + \frac{7}{3^{2} \cdot 4^{2}} + . . . . . .

n

\frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + . . .

n

\frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + . . . . . . . . .

Find the sum to n terms of the series $\frac{3}{1^{2} \times 2^{2}} + \frac{5}{2^{2} \times 3^{3}} + \frac{7}{3^{2} \times 4^{2}} . . . . . .$ is

\frac{3}{1^{2}} + \frac{5}{1^{2} + 2^{2}} + \frac{7}{1^{2} + 2^{2} + 3^{2}} + . . . . .

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